Initially I wasn't too convinced about Chromecast until I saw it in operation while visiting some friends.
What I really like about it is its ability to queue YouTube videos from multiple devices connected simultaneously. This was great at a house party where people were able to pick music videos on their smartphone or tablet to add to the queue, just like with a Jukebox but without having to walk up to it. The queue could also be edited from any connected handset.
Another common use I saw while visiting the US is people using it for Pandora internet radio, as most people there have their TV connected to a fairly powerful speaker system. During playback, Chromecast shows the song information on the screen. When I first saw it, I had no idea the owner was running Pandora from her phone until I asked what set top box is she using and she said Chromecast.
I have an Ezcast dongle on my TV and despite it claiming to be superior to Chromecast, personally I find that each has its pros and cons. For example, Ezcast supports screen mirroring (via Miracast) which is great for mirroring a laptop screen to the TV. With a compatible phone, it adds the ability to cast most apps, such as the native video and music players as well as codecs that the Chromecast doesn't support. On the other hand, despite Ezcast's screen mirroring capability, video playback in screen mirroring mode from a laptop is quite stuttery, especially in 1080p mode. So even though it provides the ability to watch video on demand services that don't work with Chromecast, it's still no match for a proper wireless HDMI sender, but still useful for those who are not after fluid-smooth video.